Singular BGG sequences for the even orthogonal case
Krump, Lukáš ; Souček, Vladimír
Archivum Mathematicum, Tome 042 (2006), p. 267-278 / Harvested from Czech Digital Mathematics Library
Access to full text
Full (PDF)

Locally exact complexes of invariant differential operators are constructed on the homogeneous model for a parabolic geometry for the even orthogonal group. The tool used for the construction is the Penrose transform developed by R. Baston and M. Eastwood. Complexes constructed here belong to the singular infinitesimal character.

Publié le : 2006-01-01
Classification:  22Exx,  58Jxx 
@article{108033,
     author = {Luk\'a\v s Krump and Vladim\'\i r Sou\v cek},
     title = {Singular BGG sequences for the even orthogonal case},
     journal = {Archivum Mathematicum},
     volume = {042},
     year = {2006},
     pages = {267-278},
     zbl = {1164.58317},
     mrnumber = {2322413},
     language = {en},
     url = {http://dml.mathdoc.fr/item/108033}
}

Krump, Lukáš; Souček, Vladimír. Singular BGG sequences for the even orthogonal case. Archivum Mathematicum, Tome 042 (2006) pp. 267-278. http://gdmltest.u-ga.fr/item/108033/

Baston R. Quaternionic complexes, J. Geom. Phys. 8 (1992), 29–52. (1992) | MR 1165872 | Zbl 0764.53022

Baston R. J.; Eastwood M. G. Penrose transform; Its interaction with representation theory, Clarendon Press, Oxford, 1989. (1989) | MR 1038279 | Zbl 0726.58004

Calderbank D. M. J.; Diemer T. Differential invariants and curved Bernstein–Gelfand–Gelfand sequences, J. Reine angew. Math. 537 (2001), 67–103. | MR 1856258 | Zbl 0985.58002

Čap A. Two constructions with parabolic geometries, preprint, arXiv:math.DG/0504389 | MR 2287124 | Zbl 1120.53013

Čap A.; Schichl H. Parabolic geometries and canonical Cartan connections, Hokkaido Math. J. 29 3 (2000), 453–505. | MR 1795487 | Zbl 0996.53023

Čap A.; Slovák J.; Souček V. Bernstein-Gelfand-Gelfand sequences, Ann. of Math. (2) 154 1 (2001), 97–113. | MR 1847589

Colombo F.; Sabadini A.; Sommen F.; Struppa D. Analysis of Dirac systems and computational algebra, Birkhäuser, Basel, 2004. | MR 2089988 | Zbl 1064.30049

Franek P. Generalized Verma module homomorphisms in singular character, submitted to Proc. of the Winter School ’Geometry and Physics’, Srni, 2006. | MR 2322409 | Zbl 1164.22310

Krump L. Construction of BGG sequences for AHS structures, Comment. Math. Univ. Carolin. 42 1 (2001), 31–52, | MR 1825371 | Zbl 1054.53071

Krump L.; Souček V. Hasse diagrams for parabolic geometries, Proc. of ’The 22nd Winter School ’Geometry and Physics’, Srní 2002, Rend. Circ. Mat. Palermo (2) Suppl. 71 (2003). | MR 1982440 | Zbl 1047.53014

Nacinovich M. Complex analysis and complexes of differential operators, LNM 950, Springer-Verlag, Berlin, 1980. (1980) | MR 0672785

Sharpe R. W. Differential geometry, Grad. Texts in Math. 166 (1997). (1997) | MR 1453120 | Zbl 0876.53001

Slovák J. Parabolic geometries, Research Lecture Notes, Part of DrSc. Dissertation, Preprint IGA 11/97, electronically available at www.maths.adelaide.edu.au.

Šmíd D. The BGG diagram for contact orthogonal geometry of even dimension, Acta Univ. Carolin. Math. Phys. 45 (2004), 79–96. | MR 2109696 | Zbl 1138.17310